U.S. citizen seeks advice on getting work visa and cheap medical tests

I have been offered a teaching position at a Saudi university for September. My employer sent a list of visa agents in the U.S. and recommended I use one to get the work visa. He said one based in Washington, D.C. would be best.(I live in Illinois.)There are a dozen listed on my list for the Washington,D.C. area and others listed for other areas such as New York and Virginia. The list just has mailing addresses and phone numbers, no email addresses.
How do I choose a capable visa agent? Can anyone here recommend one? Do they charge a fee? If so, how much? And finally, how can I get the required medical tests done cheaply?
I have acquired a work visa for Saudi before, but the process is always arduous and the medical tests are an expensive hassle. I'd like to get this done as cheaply and easily as possible. Any help would be greatly appreciated. Thank you kindly.